Informatics and Applications
2026, Volume 20, Issue 1, pp 64-72
ORDERING OF MULTIVARIATE LONGITUDINAL DATA BASED ON COINTEGRATION ANALYSIS
Abstract
In the processing of longitudinal data, multivariate cointegration analysis methods deserve for special attention identifying long-term relationships between several nonstationary time series. In relation to the problems of econometrics, the article discusses the application of cointegration analysis to the ranking of objects based on a single indicator: the degrees of connectivity between the components of an observed multidimensional time series.
With this approach, it is natural to process a couple of time series. For higher-dimensional cases, it is proposed to apply specific data transformations to obtain the required structure of the object or turn to multidimensional cointegration analysis followed by a multidimensional ordering problem formulation. The data for the experiments contained detailed characteristics of investment activity by region: investment in fixed assets (Inv), gross regional product (Prod), and number of employed people. To find a cointegrating vector for the data of each subject, a regression of the Prod process on Inv is constructed, for which the coefficient at Inv can be interpreted as the relate coefficient r processes of investment and gross regional product with the subsequent use of this characteristic as an indicator of the efficiency of economic activity, in particular, to build a rating of regions. In the course of regression analysis, not only an estimate of r* is obtained but also its selective characteristics become known, i. e., it becomes possible to get an idea of the significance of differences between individual r* values.
[+] References (18)
- Fitzmaurice, G. M., N. M. Laird, and J. H. Ware. 2011. Applied longitudinal analysis. 2nd ed. Hoboken, NJ: Wiley. 752 p.
- Bandyopadhyay, S., B. Ganguli, and A. Chatterjee. 2011. A review of multivariate longitudinal data analysis. Stat. Methods Med. Res. 20(4):299-330. doi: 10.1177/ 0962280209340191.
- Verbeke, G., S. Fieuws, G. Molenberghs, and M. Davidian. 2014. The analysis of multivariate longitudinal data: A review. Stat. Methods Med. Res. 23(1):42- 59. doi: 10.1177/0962280212445834.
- Krivenko, M. P. 2020. Bayesovskaya klassifikatsiya seriy mnogomernykh dannykh [Bayesian classification of serial multivariate data]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 30(1):34-45. doi: 10.14357/ 08696527200103. EDN: DSSUBO.
- Fieuws, S., G. Verbeke, and G. Molenberghs. 2007. Random-effects models for multivariate repeated measures. Stat. Methods Med. Res. 16(5):387-397. doi: 10.1177/0962280206075305.
- Engle, R. F., and C.W J. Granger. 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica 55(2):251-276. doi: 10.2307/ 1913236.
- Granger, C. J., and P. Newbold. 1974. Spurious regressions in econometrics. J. Econometrics 2(2):111-120. doi: 10.1016/0304-4076(74)90034-7.
- Pfaff, B. 2008. Analysis of integrated and cointegrated time series with R. 2nd ed. New York, NY Springer. 190 p. doi: 10.1007/978-0-387-75967-8.
- Stock, J. H. 1987. Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica 55(5):1035-1056. doi: 10.2307/1911260.
- Granger, C. W J. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econo- metrica 37(3):424-438. doi: 10.2307/1912791.
- Campbell, J. Y., and P. Perron. 1991. Pitfalls and opportunities: What macroeconomists should know about unit roots. NBER Macroecon. Annu. 6:141-218.
- Johansen, S. 1995. Likelihood-based inference in cointegrated vector autoregressive models. Advanced texts in econometrics ser. Oxford: Oxford University Press. 280 p.
- Bezborodova, A.V. 2008. Ob ekonometricheskoy modeli analiza i prognozirovaniya investitsiy v osnovnoy kapital [On an econometric model for analyzing and forecasting investments in fixed capital]. Ekonomika, modelirovanie, prognozirovanie [Economics, Modeling, Forecasting] 2:302-309. EDN: CPTSUK.
- Belyanichev, V. G., and A. F Savderova. 2019. Otsenka vliyaniya investitsiy v osnovnoy kapital na ob"em valovogo regional'nogo produkta [Assessment of the impact of real fixed capital formation on the volume of the gross regional product]. Oeconomia etjus [Economics and Law] 1:15-21. EDN: ZALDPN.
- Dolgunova, A. Ts. 2023. Otsenka vliyaniya investitsiy v osnovnoy kapital na ekonomicheskiy rost severnykh sub"ektov Rossiyskoy Federatsii [Assessment of the impact of investment in fixed assets on the economic growth of the northern subjects of the Russian Federation]. Stati- stika iekonomika [Statistics and Economics] 20(6):35-47. doi: 10.21686/2500-3925-2023-6-35-47. EDN: TXYLJJ.
- Banerjee, A., J.J. Dolado, J. W Galbraith, and D. F Hendry. 1993. Co-integration, error correction, and the econometric analysis of non-stationary data. Oxford: Oxford University Press. 329 p.
- Cochrane, J. H. 1991. A critique of the application of unit root tests. J. Economic Dynamics Control 15(2):275-284. doi: 10.1016/0165- 1889(91)90013-Q.
- Krivenko, M. P 2025. Sravnitel'nyy analiz testov stabil'nosti sistemy massovogo obsluzhivaniya [Comparative analysis of queuing system stability tests]. Informatika i ee Primeneniya - Inform. Appl. 19(1):61-66. doi: 10.14357/19922264250108. EDN: XDTUNK.
[+] About this article
Title
ORDERING OF MULTIVARIATE LONGITUDINAL DATA BASED ON COINTEGRATION ANALYSIS
Journal
Informatics and Applications
2026, Volume 20, Issue 1, pp 64-72
Cover Date
2026-01-04
DOI
10.14357/19922264260108
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
regression analysis; spurious regression; cointegration analysis; relate coefficient; regional economy; investments; gross regional product; number of employed persons; statistics with R; tests for stationarity; object ordering
Authors
M. P. Krivenko 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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